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Volumn 229, Issue 22, 2010, Pages 8333-8363

Time-dependent generalized polynomial chaos

Author keywords

Monte Carlo simulation; Polynomial chaos; Stochastic differential equations; Time dependence

Indexed keywords

DIFFERENTIAL EQUATIONS; INTEGRAL EQUATIONS; INTEGRATION; INTELLIGENT SYSTEMS; MONTE CARLO METHODS; ORTHOGONAL FUNCTIONS; PROBABILITY DENSITY FUNCTION; PROBABILITY DISTRIBUTIONS; STOCHASTIC SYSTEMS;

EID: 77956414223     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2010.07.020     Document Type: Article
Times cited : (170)

References (35)
  • 2
    • 36849138331 scopus 로고
    • Direct-interaction approximation for a system of several interacting simple shear waves
    • Kraichnan R.H. Direct-interaction approximation for a system of several interacting simple shear waves. The Physics of Fluids 1963, 6(11):1603-1609.
    • (1963) The Physics of Fluids , vol.6 , Issue.11 , pp. 1603-1609
    • Kraichnan, R.H.1
  • 3
    • 0013201448 scopus 로고
    • Dynamical properties of truncated Wiener-Hermite expansions
    • Orszag S.A., Bissonnette L.R. Dynamical properties of truncated Wiener-Hermite expansions. The Physics of Fluids 1967, 10(12):2603-2613.
    • (1967) The Physics of Fluids , vol.10 , Issue.12 , pp. 2603-2613
    • Orszag, S.A.1    Bissonnette, L.R.2
  • 5
    • 0037249229 scopus 로고    scopus 로고
    • The Wiener-Askey polynomial chaos for stochastic differential equations
    • Xiu D., Karniadakis G. The Wiener-Askey polynomial chaos for stochastic differential equations. SIAM Journal on Scientific Computing 2002, 24(2):619-644.
    • (2002) SIAM Journal on Scientific Computing , vol.24 , Issue.2 , pp. 619-644
    • Xiu, D.1    Karniadakis, G.2
  • 6
    • 0037408312 scopus 로고    scopus 로고
    • Modeling uncertainty in flow simulations via generalized polynomial chaos
    • Xiu D., Karniadakis G. Modeling uncertainty in flow simulations via generalized polynomial chaos. Journal of Computational Physics 2003, 187(1):137-167.
    • (2003) Journal of Computational Physics , vol.187 , Issue.1 , pp. 137-167
    • Xiu, D.1    Karniadakis, G.2
  • 7
    • 0041782621 scopus 로고    scopus 로고
    • Protein labeling reactions in electrochemical microchannel flow: Numerical simulation and uncertainty propagation
    • Debusschere B., Najm H., Matta A., Knio O., Ghanem R., Le Maître O. Protein labeling reactions in electrochemical microchannel flow: Numerical simulation and uncertainty propagation. Physics of Fluids 2003, 15:2238-2250.
    • (2003) Physics of Fluids , vol.15 , pp. 2238-2250
    • Debusschere, B.1    Najm, H.2    Matta, A.3    Knio, O.4    Ghanem, R.5    Le Maître, O.6
  • 8
    • 19044387138 scopus 로고    scopus 로고
    • Using stochastic analysis to capture unstable equilibrium in natural convection
    • Asokan B.V., Zabaras N. Using stochastic analysis to capture unstable equilibrium in natural convection. Journal of Computational Physics 2005, 108:134-153.
    • (2005) Journal of Computational Physics , vol.108 , pp. 134-153
    • Asokan, B.V.1    Zabaras, N.2
  • 9
    • 33746436285 scopus 로고    scopus 로고
    • Uncertainty propagation in cfd using polynomial chaos decomposition
    • Knio O.V., Le Maître O. Uncertainty propagation in cfd using polynomial chaos decomposition. Fluid Dynamics Research 2006, 38:614-640.
    • (2006) Fluid Dynamics Research , vol.38 , pp. 614-640
    • Knio, O.V.1    Le Maître, O.2
  • 11
    • 63449137570 scopus 로고    scopus 로고
    • Uncertainty quantification and polynomial chaos techniques in computational fluid dynamics
    • Najim H.N. Uncertainty quantification and polynomial chaos techniques in computational fluid dynamics. Annual Review of Fluid Mechanics 2009, 41:35-52.
    • (2009) Annual Review of Fluid Mechanics , vol.41 , pp. 35-52
    • Najim, H.N.1
  • 12
    • 33745013166 scopus 로고    scopus 로고
    • Beyond Wiener-Askey expansions: handling arbitrary PDFs
    • Wan X., Karniadakis G. Beyond Wiener-Askey expansions: handling arbitrary PDFs. Journal of Scientific Computing 2006, 27(1-3):455-464.
    • (2006) Journal of Scientific Computing , vol.27 , Issue.1-3 , pp. 455-464
    • Wan, X.1    Karniadakis, G.2
  • 13
    • 16244409214 scopus 로고    scopus 로고
    • Physical systems with random uncertainties: chaos representations with arbitrary probability measure
    • Soize C., Ghanem R. Physical systems with random uncertainties: chaos representations with arbitrary probability measure. SIAM Journal of Scientific Computing 2004, 26(2):395-410.
    • (2004) SIAM Journal of Scientific Computing , vol.26 , Issue.2 , pp. 395-410
    • Soize, C.1    Ghanem, R.2
  • 14
  • 15
    • 33744543472 scopus 로고    scopus 로고
    • Wiener chaos expansions and numerical solutions of randomly forced equations of fluid mechanics
    • Hou T.Y., Luo W., Rozovskii B., Zhou H.-M. Wiener chaos expansions and numerical solutions of randomly forced equations of fluid mechanics. Journal of Computational Physics 2006, 216:687-706.
    • (2006) Journal of Computational Physics , vol.216 , pp. 687-706
    • Hou, T.Y.1    Luo, W.2    Rozovskii, B.3    Zhou, H.-M.4
  • 16
    • 21444449245 scopus 로고    scopus 로고
    • An adaptive multi-element generalized polynomial chaos method for stochastic differential equations
    • Wan X., Karniadakis G. An adaptive multi-element generalized polynomial chaos method for stochastic differential equations. Journal of Computational Physics 2005, 209(2):617-642.
    • (2005) Journal of Computational Physics , vol.209 , Issue.2 , pp. 617-642
    • Wan, X.1    Karniadakis, G.2
  • 17
    • 33646672689 scopus 로고    scopus 로고
    • Spectral and multiresolution Wiener expansions of oscillatory stochastic processes
    • Pettit C.L., Beran P.S. Spectral and multiresolution Wiener expansions of oscillatory stochastic processes. Journal of Sound and Vibrations 2006, 294:752-779.
    • (2006) Journal of Sound and Vibrations , vol.294 , pp. 752-779
    • Pettit, C.L.1    Beran, P.S.2
  • 18
    • 55649083702 scopus 로고    scopus 로고
    • An alternative unsteady adaptive stochastic finite element formulation based on interpolation at constant phase
    • Witteveen J.A.S., Bijl H. An alternative unsteady adaptive stochastic finite element formulation based on interpolation at constant phase. Computer Methods in Applied Mechanics and Engineering 2008, 198:578-591.
    • (2008) Computer Methods in Applied Mechanics and Engineering , vol.198 , pp. 578-591
    • Witteveen, J.A.S.1    Bijl, H.2
  • 19
    • 67849124148 scopus 로고    scopus 로고
    • Effect of randomness on multi-frequency aeroelastic response resolved by unsteady adaptive finite elements
    • Witteveen J.A.S., Bijl H. Effect of randomness on multi-frequency aeroelastic response resolved by unsteady adaptive finite elements. Journal of Computational Physics 2009, 228:7025-7045.
    • (2009) Journal of Computational Physics , vol.228 , pp. 7025-7045
    • Witteveen, J.A.S.1    Bijl, H.2
  • 20
    • 67650938584 scopus 로고    scopus 로고
    • A TVD uncertainty quantification method with bounded error applied to transonic airfoil flutter
    • Witteveen J.A.S., Bijl H. A TVD uncertainty quantification method with bounded error applied to transonic airfoil flutter. Communications in Computational Physics 2009, 6:406-432.
    • (2009) Communications in Computational Physics , vol.6 , pp. 406-432
    • Witteveen, J.A.S.1    Bijl, H.2
  • 21
    • 0000148817 scopus 로고
    • The orthogonal development of non-linear functionals in series of Fourier-Hermite functionals
    • Cameron R.H., Martin W.T. The orthogonal development of non-linear functionals in series of Fourier-Hermite functionals. Annals of Mathematics 1947, 48(2):385-392.
    • (1947) Annals of Mathematics , vol.48 , Issue.2 , pp. 385-392
    • Cameron, R.H.1    Martin, W.T.2
  • 22
    • 84918385534 scopus 로고
    • Orthogonal functionals of the Poisson process
    • Ogura H. Orthogonal functionals of the Poisson process. IEEE Transactions on Information Theory 1972, 18(4):473-481.
    • (1972) IEEE Transactions on Information Theory , vol.18 , Issue.4 , pp. 473-481
    • Ogura, H.1
  • 24
    • 41149139344 scopus 로고    scopus 로고
    • Efficient quantification of the effect of uncertainties in advection-diffusion problems using polynomial chaos
    • Witteveen J.A.S., Bijl H. Efficient quantification of the effect of uncertainties in advection-diffusion problems using polynomial chaos. Numerical Heat Transfer B - Fundamental 2008, 53:437-465.
    • (2008) Numerical Heat Transfer B - Fundamental , vol.53 , pp. 437-465
    • Witteveen, J.A.S.1    Bijl, H.2
  • 25
    • 0004911282 scopus 로고
    • Symbolic calculus of the Wiener process and Wiener-Hermite functionals
    • Imamura T., Meecham W.C., Siegel A. Symbolic calculus of the Wiener process and Wiener-Hermite functionals. Journal of Mathematical Physics 1965, 6(5):695-706.
    • (1965) Journal of Mathematical Physics , vol.6 , Issue.5 , pp. 695-706
    • Imamura, T.1    Meecham, W.C.2    Siegel, A.3
  • 26
    • 0344522746 scopus 로고
    • The Wiener-Hermite expansion with time-dependent ideal random function
    • Doi M., Imamura T. The Wiener-Hermite expansion with time-dependent ideal random function. Progress of Theoretical Physics 1969, 41(2):358-366.
    • (1969) Progress of Theoretical Physics , vol.41 , Issue.2 , pp. 358-366
    • Doi, M.1    Imamura, T.2
  • 27
    • 77956415032 scopus 로고
    • The Wiener-Hermite expansion with time-dependent ideal random function. II - The three-mode model
    • Tanaka S., Imamura T. The Wiener-Hermite expansion with time-dependent ideal random function. II - The three-mode model. Progress of Theoretical Physics 1971, 45(4):1098-1105.
    • (1971) Progress of Theoretical Physics , vol.45 , Issue.4 , pp. 1098-1105
    • Tanaka, S.1    Imamura, T.2
  • 28
    • 36849113534 scopus 로고
    • Time-dependent Wiener-Hermite expansion for the nearly Gaussian turbulence in the Burgers' system
    • Yano M., Imamura T. Time-dependent Wiener-Hermite expansion for the nearly Gaussian turbulence in the Burgers' system. Physics of Fluids 1972, 15(4):708-710.
    • (1972) Physics of Fluids , vol.15 , Issue.4 , pp. 708-710
    • Yano, M.1    Imamura, T.2
  • 29
    • 85190211229 scopus 로고    scopus 로고
    • Time-Dependent Polynomial Chaos, Master's Thesis, Delft University of Technology, November
    • P. Vos, Time-Dependent Polynomial Chaos, Master's Thesis, Delft University of Technology, November 2006.
    • (2006)
    • Vos, P.1
  • 32
    • 85190228241 scopus 로고    scopus 로고
    • Time-Dependent Generalized Polynomial Chaos - Applied to the Kraichnan-Orszag Three-Mode Problem, Technical Report, Faculty of Aerospace Engineering, TU Delft
    • J.B. Van der Steen, Time-Dependent Generalized Polynomial Chaos - Applied to the Kraichnan-Orszag Three-Mode Problem, Technical Report, Faculty of Aerospace Engineering, TU Delft, 2008.
    • (2008)
    • Van der Steen, J.B.1
  • 34
    • 52749087886 scopus 로고    scopus 로고
    • The multi-element probabilistic collocation method (ME-PCM): error analysis and applications
    • Foo J., Wan X., Karniadakis G. The multi-element probabilistic collocation method (ME-PCM): error analysis and applications. Journal Computational Physics 2008, 227(22):9572-9595.
    • (2008) Journal Computational Physics , vol.227 , Issue.22 , pp. 9572-9595
    • Foo, J.1    Wan, X.2    Karniadakis, G.3
  • 35
    • 4043118237 scopus 로고    scopus 로고
    • Evaluation of uncertainty quantification of power system models: the probabilistic collocation method
    • Hockenberry J.R., Lesieutre B.C. Evaluation of uncertainty quantification of power system models: the probabilistic collocation method. IEEE Transactions on Power Systems 2004, 19(3):1483-1491.
    • (2004) IEEE Transactions on Power Systems , vol.19 , Issue.3 , pp. 1483-1491
    • Hockenberry, J.R.1    Lesieutre, B.C.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.